Cellular contractility and substrate elasticity: a numerical investigation of the actin cytoskeleton and cell adhesion

The role of the nucleus for cell mechanics: an elastic phase field approach

The nucleus of eukaryotic cells typically makes up around 30% of the cell volume and has significantly different mechanics, which can make it effectively up to ten times stiffer than the surrounding cytoplasm. Therefore it is an important element for cell mechanics, but a quantitative understanding of its mechanical role during whole cell dynamics is largely missing. Here we demonstrate that elastic phase fields can be used to describe dynamical cell processes in adhesive or confining environments in which the nucleus acts as a stiff inclusion in an elastic cytoplasm. We first introduce and verify our computational method and then study several prevalent cell-mechanical measurement methods. For cells on adhesive patterns, we find that nuclear stress is shielded by the adhesive pattern. For cell compression between two parallel plates, we obtain force-compression curves that allow us to extract an effective modulus for the cell-nucleus composite. For micropipette aspiration, the effect of the nucleus on the effective modulus is found to be much weaker, highlighting the complicated interplay between extracellular geometry and cell mechanics that is captured by our approach. We also show that our phase field approach can be used to investigate the effects of Kelvin-Voigt-type viscoelasticity and cortical tension.

Revelation of adhesive proteins affecting cellular contractility through reference-free traction force microscopy

Over the past few decades, the critical role played by cellular contractility associated mechanotransduction in the regulation of cell functions has been revealed. In this case, numerous biomaterials have been chemically or structurally designed to manipulate cell behaviors through the regulation of cellular contractility. In particular, adhesive proteins including fibronectin, poly-L-lysine and collagen type I have been widely applied in various biomaterials to improve cell adhesion. Therefore, clarifying the effects of adhesive proteins on cellular contractility has been valuable for the development of biomaterial design. In this study, reference-free traction force microscopy with a well-organized microdot array was designed and prepared to investigate the relationship between adhesive proteins, cellular contractility, and mechanotransduction. The results showed that fibronectin and collagen type I were able to promote the assembly of focal adhesions and further enhance cellular contraction and YAP activity. In contrast, although poly-L-lysine supported cell spreading and elongation, it was inefficient at inducing cell contractility and activating YAP. Additionally, compared with cellular morphogenesis, cellular contraction was essential for YAP activation.

Programmable and Reversible Integrin-Mediated Cell Adhesion Reveals Hysteresis in Actin Kinetics that Alters Subsequent Mechanotransduction

Dynamically evolving adhesions between cells and extracellular matrix (ECM) transmit time-varying signals that control cytoskeletal dynamics and cell fate. Dynamic cell adhesion and ECM stiffness regulate cellular mechanosensing cooperatively, but it has not previously been possible to characterize their individual effects because of challenges with controlling these factors independently. Therefore, a DNA-driven molecular system is developed wherein the integrin-binding ligand RGD can be reversibly presented and removed to achieve cyclic cell attachment/detachment on substrates of defined stiffness. Using this culture system, it is discovered that cyclic adhesion accelerates F-actin kinetics and nuclear mechanosensing in human mesenchymal stem cells (hMSCs), with the result that hysteresis can completely change how hMSCs transduce ECM stiffness. Results are dramatically different from well-known results for mechanotransduction on static substrates, but are consistent with a mathematical model of F-actin fragments retaining structure following loss of integrin ligation and participating in subsequent repolymerization. These findings suggest that cyclic integrin-mediated adhesion alters the mechanosensing of ECM stiffness by hMSCs through transient, hysteretic memory that is stored in F-actin.

The fibrous character of pericellular matrix mediates cell mechanotransduction

Cells in solid tissues sense and respond to mechanical signals that are transmitted through extracellular matrix (ECM) over distances that are many times their size. This long-range force transmission is known to arise from strain-stiffening and buckling in the collagen fiber ECM network, but must also pass through the denser pericellular matrix (PCM) that cells form by secreting and compacting nearby collagen. However, the role of the PCM in the transmission of mechanical signals is still unclear. We therefore studied an idealized computational model of cells embedded within fibrous collagen ECM and PCM. Our results suggest that the smaller network pore sizes associated with PCM attenuates tension-driven collagen-fiber alignment, undermining long-range force transmission and shielding cells from mechanical stress. However, elongation of the cell body or anisotropic cell contraction can compensate for these effects to enable long distance force transmission. Results are consistent with recent experiments that highlight an effect of PCM on shielding cells from high stresses. Results have implications for the transmission of mechanical signaling in development, wound healing, and fibrosis.

A multi-scale clutch model for adhesion complex mechanics

Cell-matrix adhesion is a central mechanical function to a large number of phenomena in physiology and disease, including morphogenesis, wound healing, and tumor cell invasion. Today, how single cells respond to different extracellular cues has been comprehensively studied. However, how the mechanical behavior of the main individual molecules that form an adhesion complex cooperatively responds to force within the adhesion complex is still poorly understood. This is a key aspect of cell adhesion because how these cell adhesion molecules respond to force determines not only cell adhesion behavior but, ultimately, cell function. To answer this question, we develop a multi-scale computational model for adhesion complexes mechanics. We extend the classical clutch hypothesis to model individual adhesion chains made of a contractile actin network, a talin rod, and an integrin molecule that binds at individual adhesion sites on the extracellular matrix. We explore several scenarios of integrins dynamics and analyze the effects of diverse extracellular matrices on the behavior of the adhesion molecules and on the whole adhesion complex. Our results describe how every single component of the adhesion chain mechanically responds to the contractile actomyosin force and show how they control the traction forces exerted by the cell on the extracellular space. Importantly, our computational results agree with previous experimental data at the molecular and cellular levels. Our multi-scale clutch model presents a step forward not only to further understand adhesion complexes mechanics but also to impact, e.g., the engineering of biomimetic materials, tissue repairment, or strategies to arrest tumor progression.

Engineering Strategies to Move from Understanding to Steering Renal Tubulogenesis

Rebuilding the kidney in the context of tissue engineering offers a major challenge as the organ is structurally complex and has a high variety of specific functions. Recreation of kidney function is inherently connected to the formation of tubules since the functional subunit of the kidney, the nephron, is based on tubular structures. In vivo, tubulogenesis culminates in a perfectly shaped, patterned, and functional renal tubule via different morphogenic processes that depend on delicately orchestrated chemical, physical, and mechanical interactions between cells and between cells and their microenvironment. This review summarizes the current understanding of the role of the microenvironment in the morphogenic processes involved in in vivo renal tubulogenesis. We highlight the current state-of-the-art of renal tubular engineering and provide a view on the design elements that can be extracted from these studies. Next, we discuss how computational modeling can aid in specifying and identifying design parameters and provide directions on how these design parameters can be incorporated in biomaterials for the purpose of engineering renal tubulogenesis. Finally, we propose that a step-by-step reciprocal interaction between understanding and engineering is necessary to effectively guide renal tubulogenesis. Impact statement Tubular tissue engineering lies at the foundation of regenerating kidney tissue function, as the functional subunit of the kidney, the nephron, is based on tubular structures. Guiding renal tubulogenesis toward functional renal tubules requires in-depth knowledge of the developmental processes that lead to the formation of native tubules as well as engineering approaches to steer these processes. In this study, we review the role of the microenvironment in the developmental processes that lead to functional renal tubules and give directions how this knowledge can be harnessed for biomaterial-based tubular engineering using computational models.

Mechanobiology of the relocation of proteins in advecting cells: in vitro experiments, multi-physics modeling, and simulations

Cell motility-a cellular behavior of paramount relevance in embryonic development, immunological response, metastasis, or angiogenesis-demands a mechanical deformation of the cell membrane and influences the surface motion of molecules and their biochemical interactions. In this work, we develop a fully coupled multi-physics model able to capture and predict the protein flow on endothelial advecting plasma membranes. The model has been validated against co-designed in vitro experiments. The complete picture of the receptor dynamics has been understood, and limiting factors have been identified together with the laws that regulate receptor polarization. This computational approach might be insightful in the prediction of endothelial cell behavior in different tumoral environments, circumventing the time-consuming and expensive empirical characterization of each tumor.

Modeling Receptor Motility along Advecting Lipid Membranes

This work aims to overview multiphysics mechanobiological computational models for receptor dynamics along advecting cell membranes. Continuum and statistical models of receptor motility are the two main modeling methodologies identified in reviewing the state of the art. Within the former modeling class, a further subdivision based on different biological purposes and processes of proteins’ motion is recognized; cell adhesion, cell contractility, endocytosis, and receptor relocations on advecting membranes are the most relevant biological processes identified in which receptor motility is pivotal. Numerical and/or experimental methods and approaches are highlighted in the exposure of the reviewed works provided by the literature, pertinent to the topic of the present manuscript. With a main focus on the continuum models of receptor motility, we discuss appropriate multiphyisics laws to model the mass flux of receptor proteins in the reproduction of receptor relocation and recruitment along cell membranes to describe receptor–ligand chemical interactions, and the cell’s structural response. The mass flux of receptor modeling is further supported by a discussion on the methodology utilized to evaluate the protein diffusion coefficient developed over the years.

Actomyosin contractility and buckling of microtubules in nucleation, growth and disassembling of focal adhesions

Building up and maintenance of cytoskeletal structure in living cells are force-dependent processes involving a dynamic chain of polymerization and depolymerization events, which are also at the basis of cells’ remodelling and locomotion. All these phenomena develop by establishing cell–matrix interfaces made of protein complexes, known as focal adhesions, which govern mechanosensing and mechanotransduction mechanisms mediated by stress transmission between cell interior and external environment. Within this framework, by starting from a work by Cao et al. (Biophys J 109:1807–1817, 2015), we here investigate the role played by actomyosin contractility of stress fibres in nucleation, growth and disassembling of focal adhesions. In particular, we propose a tensegrity model of an adherent cell incorporating nonlinear elasticity and unstable behaviours, which provides a new kinematical interpretation of cellular contractile forces and describes how stress fibres, microtubules and adhesion plaques interact mechanobiologically. The results confirm some experimental evidences and suggest how the actomyosin contraction level could be exploited by cells to actively control their adhesion, eventually triggering cytoskeleton reconfigurations and migration processes observed in both physiological conditions and diseases.

Finite Element Models of Osteocytes and Their Load-Induced Activation

PURPOSE OF REVIEW

Osteocytes are the conductors of bone adaptation and remodelling. Buried inside the calcified matrix, they sense mechanical cues and signal osteoclasts in case of low activity, and osteoblasts when stresses are high. How do osteocytes detect mechanical stress? What physical signal do they perceive? Finite element analysis is a useful tool to address these questions as it allows calculating stresses, strains and fluid flow where they cannot be measured. The purpose of this review is to evaluate the capabilities and challenges of finite element models of bone, in particular the osteocytes and load-induced activation mechanisms.

RECENT FINDINGS

High-resolution imaging and increased computational power allow ever more detailed modelling of osteocytes, either in isolation or embedded within the mineralised matrix. Over the years, homogeneous models of bone and osteocytes got replaced by heterogeneous and microstructural models, including, e.g. the lacuno-canalicular network and the cytoskeleton. The lacuno-canalicular network induces strain amplifications and the osteocyte protrusions seem to be stimulated much more than the cell body, both by strain and fluid flow. More realistic cell geometries, like minute constrictions of the canaliculi, increase this effect. Microstructural osteocyte models describe the transduction of external stimuli to the nucleus. Supracellular multiscale models (e.g. of a tunnelling osteon) allow to study differential loading of osteocytes and to distinguish between strain and fluid flow as the pivotal stimulatory cue. In the future, the finite element models may be enhanced by including chemical transport and intercellular communication between osteocytes, osteoclasts and osteoblasts.

Cellular Tango: how extracellular matrix adhesion choreographs Rac-Rho signaling and cell movement

The small GTPases Rac and Rho are known to regulate eukaryotic cell shape, promoting front protrusion (Rac) or rear retraction (Rho) of the cell edge. Such cell deformation changes the contact and adhesion of cell to the extracellular matrix (ECM), while ECM signaling through integrin receptors also affects GTPase activity. We develop and investigate a model for this three-way feedback loop in 1D and 2D spatial domains, as well as in a fully deforming 2D cell shapes with detailed adhesion-bond biophysics. The model consists of reaction-diffusion equations solved numerically with open-source software, Morpheus, and with custom-built cellular Potts model simulations. We find a variety of patterns and cell behaviors, including persistent polarity, flipped front-back cell polarity oscillations, spiral waves, and random protrusion-retraction. We show that the observed spatial patterns depend on the cell shape, and vice versa.

A Chemomechanical Model for Regulation of Contractility in the Embryonic Brain Tube

Morphogenesis is regulated by genetic, biochemical, and biomechanical factors, but the feedback controlling the interactions between these factors remains poorly understood. A previous study has found that compressing the brain tube of the early chick embryo induces changes in contractility and nuclear shape in the neuroepithelial wall. Assuming this response involves mechanical feedback, we use experiments and computational modeling to investigate a hypothetical mechanism behind the observed behavior. First, we measured nuclear circularity in embryonic chick brains subjected to transverse compression. Immediately after loading, the circularity varied regionally and appeared to reflect the local state of stress in the wall. After three hours of culture with sustained compression, however, the nuclei became rounder. Exposure to a gap junction blocker inhibited this response, suggesting that it requires intercellular diffusion of a biochemical signal. We speculate that the signal regulates the contraction that occurs near the lumen, altering stress distributions and nuclear geometry throughout the wall. Simulating compression using a chemomechanical finite-element model based on this idea shows that our hypothesis is consistent with most of the experimental data. This work provides a foundation for future investigations of chemomechanical feedback in epithelia during embryonic development.

Image-derived modeling of nucleus strain amplification associated with chromatin heterogeneity

Beyond the critical role of cell nuclei in gene expression and DNA replication, they also have a significant influence on cell mechanosensation and migration. Nuclear stiffness can impact force transmission and, furthermore, act as a physical barrier to translocation across tight spaces. As such, it is of wide interest to accurately characterize nucleus mechanical behavior. In this study, we present a computational investigation of the in situ deformation of a heterogeneous chondrocyte nucleus. A methodology is developed to accurately reconstruct a three-dimensional finite-element model of a cell nucleus from confocal microscopy. By incorporating the reconstructed nucleus into a chondrocyte model embedded in pericellular and extracellular matrix, we explore the relationship between spatially heterogeneous nuclear DNA content, shear stiffness, and resultant shear strain. We simulate an externally applied extracellular matrix shear deformation and compute intranuclear strain distributions, which are directly compared with corresponding experimentally measured distributions. Simulations suggest that the mechanical behavior of the nucleus is highly heterogeneous, with a nonlinear relationship between experimentally measured grayscale values and corresponding local shear moduli (μn). Three distinct phases are identified within the nucleus: a low-stiffness mRNA-rich interchromatin phase (0.17 kPa ≤ μn ≤ 0.63 kPa), an intermediate-stiffness euchromatin phase (1.48 kPa ≤ μn ≤ 2.7 kPa), and a high-stiffness heterochromatin phase (3.58 kPa ≤ μn ≤ 4.0 kPa). Our simulations also indicate that disruption of the nuclear envelope associated with lamin A/C depletion significantly increases nuclear strain in regions of low DNA concentration. We further investigate a phenotypic shift of chondrocytes to fibroblast-like cells, a signature for osteoarthritic cartilage, by increasing the contractility of the actin cytoskeleton to a level associated with fibroblasts. Peak nucleus strains increase by 35% compared to control, with the nucleus becoming more ellipsoidal. Our findings may have broad implications for current understanding of how local DNA concentrations and associated strain amplification can impact cell mechanotransduction and drive cell behavior in development, migration, and tumorigenesis.

Physical and mechanical degradation behaviour of semi-crystalline PLLA for bioresorbable stent applications

This study presents a systematic evaluation of the physical, thermal and mechanical performance of medical-grade semi-crystalline PLLA undergoing thermally-accelerated degradation. Samples were immersed in phosphate-buffered saline solution at 50 °C for 112 days and mass loss, molecular weight, thermal properties, degree of crystallinity, FTIR and Raman spectra, tensile elastic modulus, yield stress and failure stress/strain were evaluated at consecutive time points. Samples showed a consistent reduction in molecular weight and melting temperature, a consistent increase in percent crystallinity and limited changes in glass transition temperature and mass loss. At day 49, a drastic reduction in tensile failure strain was observed, despite the fact that elastic modulus, yield and tensile strength of samples were maintained. Brittleness increase was followed by rapid increase in degradation rate. Beyond day 70, samples became too brittle to test indicating substantial deterioration of their load-bearing capacity. This study also presents a computational micromechanics framework that demonstrates that the elastic modulus of a semi-crystalline polymer undergoing degradation can be maintained, despite a reducing molecular weight through compensatory increases in percent crystallinity. This study presents novel insight into the relationship between physical properties and mechanical performance of medical-grade PLLA during degradation and could have important implications for design and development of bioresorbable stents for vascular applications.

Stem Cell Mechanobiology and the Role of Biomaterials in Governing Mechanotransduction and Matrix Production for Tissue Regeneration

Mechanobiology has underpinned many scientific advances in understanding how biophysical and biomechanical cues regulate cell behavior by identifying mechanosensitive proteins and specific signaling pathways within the cell that govern the production of proteins necessary for cell-based tissue regeneration. It is now evident that biophysical and biomechanical stimuli are as crucial for regulating stem cell behavior as biochemical stimuli. Despite this, the influence of the biophysical and biomechanical environment presented by biomaterials is less widely accounted for in stem cell-based tissue regeneration studies. This Review focuses on key studies in the field of stem cell mechanobiology, which have uncovered how matrix properties of biomaterial substrates and 3D scaffolds regulate stem cell migration, self-renewal, proliferation and differentiation, and activation of specific biological responses. First, we provide a primer of stem cell biology and mechanobiology in isolation. This is followed by a critical review of key experimental and computational studies, which have unveiled critical information regarding the importance of the biophysical and biomechanical cues for stem cell biology. This review aims to provide an informed understanding of the intrinsic role that physical and mechanical stimulation play in regulating stem cell behavior so that researchers may design strategies that recapitulate the critical cues and develop effective regenerative medicine approaches.

Cell Shape and Durotaxis Explained from Cell-Extracellular Matrix Forces and Focal Adhesion Dynamics

Many cells are small and rounded on soft extracellular matrices (ECM), elongated on stiffer ECMs, and flattened on hard ECMs. Cells also migrate up stiffness gradients (durotaxis). Using a hybrid cellular Potts and finite-element model extended with ODE-based models of focal adhesion (FA) turnover, we show that the full range of cell shape and durotaxis can be explained in unison from dynamics of FAs, in contrast to previous mathematical models. In our 2D cell-shape model, FAs grow due to cell traction forces. Forces develop faster on stiff ECMs, causing FAs to stabilize and, consequently, cells to spread on stiff ECMs. If ECM stress further stabilizes FAs, cells elongate on substrates of intermediate stiffness. We show that durotaxis follows from the same set of assumptions. Our model contributes to the understanding of the basic responses of cells to ECM stiffness, paving the way for future modeling of more complex cell-ECM interactions.

The Balance between Actomyosin Contractility and Microtubule Polymerization Regulates Hierarchical Protrusions That Govern Efficient Fibroblast-Collagen Interactions

Fibroblasts undergo a critical transformation from an initially inactive state to a morphologically different and contractile state after several hours of being embedded within a physiologically relevant three-dimensional (3D) fibrous collagen-based extracellular matrix (ECM). However, little is known about the critical mechanisms by which fibroblasts adapt themselves and their microenvironment in the earliest stage of cell-matrix interaction. Here, we identified the mechanisms by which fibroblasts interact with their 3D collagen fibrous matrices in the early stages of cell-matrix interaction and showed that fibroblasts use energetically efficient hierarchical micro/nano-scaled protrusions in these stages as the primary means for the transformation and adaptation. We found that actomyosin contractility in these protrusions in the early stages of cell-matrix interaction restricts the growth of microtubules by applying compressive forces on them. Our results show that actomyosin contractility and microtubules work in concert in the early stages of cell-matrix interaction to adapt fibroblasts and their microenvironment to one another. These early stage interactions result in responses to disruption of the microtubule network and/or actomyosin contractility that are opposite to well-known responses to late-stage disruption and reveal insight into the ways that cells adapt themselves and their ECM recursively.

Mechanical interplay between cell shape and actin cytoskeleton organization

We investigate the mechanical interplay between the spatial organization of the actin cytoskeleton and the shape of animal cells adhering on micropillar arrays. Using a combination of analytical work, computer simulations and in vitro experiments, we demonstrate that the orientation of the stress fibers strongly influences the geometry of the cell edge. In the presence of a uniformly aligned cytoskeleton, the cell edge can be well approximated by elliptical arcs, whose eccentricity reflects the degree of anisotropy of the cell's internal stresses. Upon modeling the actin cytoskeleton as a nematic liquid crystal, we further show that the geometry of the cell edge feeds back on the organization of the stress fibers by altering the length scale at which these are confined. This feedback mechanism is controlled by a dimensionless number, the anchoring number, representing the relative weight of surface-anchoring and bulk-aligning torques. Our model allows to predict both cellular shape and the internal structure of the actin cytoskeleton and is in good quantitative agreement with experiments on fibroblastoid (GDβ1, GDβ3) and epithelioid (GEβ1, GEβ3) cells.

Free-energy-based framework for early forecasting of stem cell differentiation

Commitment of stem cells to different lineages is inherently stochastic but regulated by a range of environmental bio/chemo/mechanical cues. Here, we develop an integrated stochastic modelling framework for predicting the differentiation of hMSCs in response to a range of environmental cues, including sizes of adhesive islands, stiffness of substrates and treatment with ROCK inhibitors in both growth and mixed media. The statistical framework analyses the fluctuations of cell morphologies over approximately a 24 h period after seeding the cells in the specific environment and uses the cytoskeletal free-energy distribution to forecast the lineage the hMSCs will commit to. The cytoskeletal free energy which succinctly parametrizes the biochemical state of the cell is shown to capture hMSC commitment over a range of environments while simple morphological factors such as cell shape, tractions on their own are unable to correlate with lineages hMSCs adopt.

Finite element investigation into the use of carbon fibre reinforced PEEK laminated composites for distal radius fracture fixation implants

Carbon fibre reinforced PEEK (CF/PEEK) laminates provide mechanical advantages over homogenous metal osteo-synthesis implants, e.g. radiolucency, fatigue strength and strength to weight ratio. Implants can be designed with custom anisotropic material properties, thus enabling the engineer to tailor the overall stiffness of the implant to the specific loading conditions it will experience in vivo. In the current study a multi-scale computational investigation of idealised distal radius fracture fixation plate (DRP) is conducted. Physiological loading conditions are applied to macro-scale finite element models of DRPs. The mechanical response is compared for several CF/PEEK laminate layups to examine the effect of ply layup design. The importance of ply orientation in laminated DRPs is highlighted. A high number of 0° plies near the outer surfaces results in a greater bending strength while the addition of 45° plies increases the torsional strength of the laminates. Intra-laminar transverse tensile failure is predicted as the primary mode of failure. A micro-mechanical analysis of the CF/PEEK microstructure uncovers the precise mechanism under-lying intra-laminar transverse tensile crack to be debonding of the PEEK matrix from carbon fibres. Plastic strains in the matrix material are not sufficiently high to result in ductile failure of the matrix. The findings of this study demonstrate the significant challenge in the design and optimisation of fibre reinforced laminated composites for orthopaedic applications, highlighting the importance of multi-scale modelling for identification of failure mechanisms.

Thermodynamic Modeling of the Statistics of Cell Spreading on Ligand-Coated Elastic Substrates

Biological spread cells exist in a perpetually fluctuating state and therefore cannot be described in terms of a unique deterministic system. For modeling approaches to provide novel insight and uncover new mechanisms that drive cell behavior, a framework is required that progresses from traditional deterministic methods (whereby simulation of an experiment predicts a single outcome). In this study, we implement a new, to our knowledge, modeling approach for the analysis of cell spreading on ligand-coated substrates, extending the framework for nonequilibrium thermodynamics of cells developed by Shishvan et al. to include active focal adhesion assembly. We demonstrate that the model correctly predicts the coupled influence of surface collagen density and substrate stiffness on cell spreading, as reported experimentally by Engler et al. Low surface collagen densities are shown to result in a high probability that cells will be restricted to low spread areas. Furthermore, elastic free energy induced by substrate deformation lowers the probability of observing a highly spread cell, and, consequentially, lower cell tractions affect the assembly of focal adhesions. Experimentally measurable observables such as cell spread area and aspect ratio can be directly postprocessed from the computed homeostatic ensemble of (several million) spread states. This allows for the prediction of mean and SDs of such experimental observables. This class of cell mechanics modeling presents a significant advance on conventional deterministic approaches.

Energy dissipation in quasi-linear viscoelastic tissues, cells, and extracellular matrix

Characterizing how a tissue's constituents give rise to its viscoelasticity is important for uncovering how hidden timescales underlie multiscale biomechanics. These constituents are viscoelastic in nature, and their mechanics must typically be assessed from the uniaxial behavior of a tissue. Confounding the challenge is that tissue viscoelasticity is typically associated with nonlinear elastic responses. Here, we experimentally assessed how fibroblasts and extracellular matrix (ECM) within engineered tissue constructs give rise to the nonlinear viscoelastic responses of a tissue. We applied a constant strain rate, "triangular-wave" loading and interpreted responses using the Fung quasi-linear viscoelastic (QLV) material model. Although the Fung QLV model has several well-known weaknesses, it was well suited to the behaviors of the tissue constructs, cells, and ECM tested. Cells showed relatively high damping over certain loading frequency ranges. Analysis revealed that, even in cases where the Fung QLV model provided an excellent fit to data, the the time constant derived from the model was not in general a material parameter. Results have implications for design of protocols for the mechanical characterization of biological materials, and for the mechanobiology of cells within viscoelastic tissues.

Simulation of actin distribution of osteoblasts on titanium pillar arrays using a bio-chemo-mechanical model

A numerical model for the adhesion of osteoblasts on titanium micropillar structures is suggested, and a function representing the concentration level of the adhesion on the pillars is constructed based on experimental observation. The introduction of this function helps a well-known bio-chemo-mechanical model to better predict the formation of actin in osteoblasts when they are laid on arrays of titanium micro-pillars of various size attached to silicon substrate. A parameter study suggests that each pillar is associated with a different pattern of adhesion. Our finding emphasises a capability of the bio-chemo-mechanical model that it can well explain the strong influence of the boundary condition on the formation of actin within the cells.

Multi-physics interactions drive VEGFR2 relocation on endothelial cells

Vascular Endothelial Growth Factor Receptor-2 (VEGFR2) is a pro-angiogenic receptor, expressed on endothelial cells (ECs). Although biochemical pathways that follow the VEGFR2 activation are well established, knowledge about the dynamics of receptors on the plasma membrane remains limited. Ligand stimulation induces the polarization of ECs and the relocation of VEGFR2, either in cell protrusions or in the basal aspect in cells plated on ligand-enriched extracellular matrix (ECM). We develop a mathematical model in order to simulate the relocation of VEGFR2 on the cell membrane during the mechanical adhesion of cells onto a ligand-enriched substrate. Co-designing the in vitro experiments with the simulations allows identifying three phases of the receptor dynamics, which are controlled respectively by the high chemical reaction rate, by the mechanical deformation rate, and by the diffusion of free receptors on the membrane. The identification of the laws that regulate receptor polarization opens new perspectives toward developing innovative anti-angiogenic strategies through the modulation of EC activation.

The Nuclear Option: Evidence Implicating the Cell Nucleus in Mechanotransduction

Biophysical stimuli presented to cells via microenvironmental properties (e.g., alignment and stiffness) or external forces have a significant impact on cell function and behavior. Recently, the cell nucleus has been identified as a mechanosensitive organelle that contributes to the perception and response to mechanical stimuli. However, the specific mechanotransduction mechanisms that mediate these effects have not been clearly established. Here, we offer a comprehensive review of the evidence supporting (and refuting) three hypothetical nuclear mechanotransduction mechanisms: physical reorganization of chromatin, signaling at the nuclear envelope, and altered cytoskeletal structure/tension due to nuclear remodeling. Our goal is to provide a reference detailing the progress that has been made and the areas that still require investigation regarding the role of nuclear mechanotransduction in cell biology. Additionally, we will briefly discuss the role that mathematical models of cell mechanics can play in testing these hypotheses and in elucidating how biophysical stimulation of the nucleus drives changes in cell behavior. While force-induced alterations in signaling pathways involving lamina-associated polypeptides (LAPs) (e.g., emerin and histone deacetylase 3 (HDAC3)) and transcription factors (TFs) located at the nuclear envelope currently appear to be the most clearly supported mechanism of nuclear mechanotransduction, additional work is required to examine this process in detail and to more fully test alternative mechanisms. The combination of sophisticated experimental techniques and advanced mathematical models is necessary to enhance our understanding of the role of the nucleus in the mechanotransduction processes driving numerous critical cell functions.

An implementation for the simulation of cells on micro-post arrays

The mechanical interaction between cells and their underlying substrates is important in understanding the processes that take place at an interface between biological tissue and the surface of implants. There have been numerous studies that examine these interactions both by experimental and numerical modeling. The bio-chemo-mechanical model for cell contractility by Deshpande et al. [1] has numerous applications and advantages. This work shows a way to implement this model in COMSOL MULTIPHYSICS® so it can be easily modified or extended. This will allow us in a next step to couple the differential system with additional external stimuli.

A phenomenological cohesive model for the macroscopic simulation of cell-matrix adhesions

Cell adhesion is crucial for cells to not only physically interact with each other but also sense their microenvironment and respond accordingly. In fact, adherent cells can generate physical forces that are transmitted to the surrounding matrix, regulating the formation of cell-matrix adhesions. The main purpose of this work is to develop a computational model to simulate the dynamics of cell-matrix adhesions through a cohesive formulation within the framework of the finite element method and based on the principles of continuum damage mechanics. This model enables the simulation of the mechanical adhesion between cell and extracellular matrix (ECM) as regulated by local multidirectional forces and thus predicts the onset and growth of the adhesion. In addition, this numerical approach allows the simulation of the cell as a whole, as it models the complete mechanical interaction between cell and ECM. As a result, we can investigate and quantify how different mechanical conditions in the cell (e.g., contractile forces, actin cytoskeletal properties) or in the ECM (e.g., stiffness, external forces) can regulate the dynamics of cell-matrix adhesions.

Fibroblasts Slow Conduction Velocity in a Reconstituted Tissue Model of Fibrotic Cardiomyopathy

Myocardial function deteriorates over the course of fibrotic cardiomyopathy, due to electrophysiological and mechanical effects of myofibroblasts that are not completely understood. Although a range of experimental model systems and associated theoretical treatments exist at the levels of isolated cardiomyocytes and planar co-cultures of myofibroblasts and cardiomyocytes, interactions between these cell types at the tissue level are less clear. We studied these interactions through an engineered heart tissue (EHT) model of fibrotic myocardium and a mathematical model of the effects of cellular composition on EHT impulse conduction velocity. The EHT model allowed for modulation of cardiomyocyte and myofibroblast volume fractions, and observation of cell behavior in a three-dimensional environment that is more similar to native heart tissue than is planar cell culture. The cardiomyocyte and myofibroblast volume fractions determined the retardation of impulse conduction (spread of the action potential) in EHTs as measured by changes of the fluorescence of the Ca²⁺ probe, Fluo-2. Interpretation through our model showed retardation far in excess of predictions by homogenization theory, with conduction ceasing far below the fibroblast volume fraction associated with steric percolation. Results point to an important multiscale structural role of myofibroblasts in attenuating impulse conduction in fibrotic cardiomyopathy.

Tissue constructs: platforms for basic research and drug discovery

The functions, form and mechanical properties of cells are inextricably linked to their extracellular environment. Cells from solid tissues change fundamentally when, isolated from this environment, they are cultured on rigid two-dimensional substrata. These changes limit the significance of mechanical measurements on cells in two-dimensional culture and motivate the development of constructs with cells embedded in three-dimensional matrices that mimic the natural tissue. While measurements of cell mechanics are difficult in natural tissues, they have proven effective in engineered tissue constructs, especially constructs that emphasize specific cell types and their functions, e.g. engineered heart tissues. Tissue constructs developed as models of disease also have been useful as platforms for drug discovery. Underlying the use of tissue constructs as platforms for basic research and drug discovery is integration of multiscale biomaterials measurement and computational modelling to dissect the distinguishable mechanical responses separately of cells and extracellular matrix from measurements on tissue constructs and to quantify the effects of drug treatment on these responses. These methods and their application are the main subjects of this review.

Single cell active force generation under dynamic loading - Part I: AFM experiments

A novel series of experiments are performed on single cells using a bespoke AFM system where the response of cells to dynamic loading at physiologically relevant frequencies is uncovered. Measured forces for the untreated cells are dramatically different to cytochalasin-D (cyto-D) treated cells, indicating that the contractile actin cytoskeleton plays a critical role in the response of cells to dynamic loading. Following a change in applied strain magnitude, while maintaining a constant applied strain rate, the compression force for contractile cells recovers to 88.9±7.8% of the steady state force. In contrast, cyto-D cell compression forces recover to only 38.0±6.7% of the steady state force. Additionally, untreated cells exhibit strongly negative (pulling) forces during unloading half-cycles when the probe is retracted. In comparison, negligible pulling forces are measured for cyto-D cells during probe retraction. The current study demonstrates that active contractile forces, generated by actin-myosin cross-bridge cycling, dominate the response of single cells to dynamic loading. Such active force generation is shown to be independent of applied strain magnitude. Passive forces generated by the applied deformation are shown to be of secondary importance, exhibiting a high dependence on applied strain magnitude, in contrast to the active forces in untreated cells.

STATEMENT OF SIGNIFICANCE

A novel series of experiments are performed on single cells using a bespoke AFM system where the response of cells to dynamic loading at physiologically relevant frequencies is uncovered. Contractile cells, which contain the active force generation machinery of the actin cytoskeleton, are shown to be insensitive to applied strain magnitude, exhibiting high resistance to dynamic compression and stretching. Such trends are not observed for cells in which the actin cytoskeleton has been chemically disrupted. These biomechanical insights have not been previously reported. This detailed characterisation of single cell active and passive stress during dynamic loading has important implications for tissue engineering strategies, where applied deformation has been reported to significantly affect cell mechanotransduction and matrix synthesis.

Single cell active force generation under dynamic loading - Part II: Active modelling insights

In Part I of this two-part study a novel single cell AFM experimental investigation reveals a complex force-strain response of cells to cyclic loading. The biomechanisms underlying such complex behaviour cannot be fully understood without a detailed mechanistic analysis incorporating the key features of active stress generation and remodelling of the actin cytoskeleton. In order to simulate untreated contractile cells an active bio-chemo-mechanical model is developed, incorporating the key features of stress fibre (SF) remodelling and active tension generation. It is demonstrated that a fading memory SF contractility model accurately captures the transient response of cells to dynamic loading. Simulations reveal that high stretching forces during unloading half-cycles (probe retraction) occur due to tension actively generated by axially oriented SFs. On the other hand, hoop oriented SFs generate tension during loading half-cycles, providing a coherent explanation for the elevated compression resistance of contractile cells. Finally, it is also demonstrated that passive non-linear visco-hyperelastic material laws, traditionally used to simulate cell mechanical behaviour, are not appropriate for untreated contractile cells, and their use should be limited to the simulation of cells in which the active force generation machinery of the actin cytoskeleton has been chemically disrupted. In summary, our active modelling framework provides a coherent understanding of the biomechanisms underlying the complex patterns of experimentally observed single cell force generation presented in the first part of this study.

STATEMENT OF SIGNIFICANCE

A novel computational investigation into the active and passive response of cells to dynamic loading is performed. An active formulation that considers key features of actin cytoskeleton active contractility and remodelling throughout the cytoplasm is implemented. Simulations provide new insights into the sub-cellular biomechanical response, providing a coherent explanation for the complex patterns of cell force uncovered experimentally in the first part of this study. Our computational models also reveal that passive non-linear visco-hyperelastic material laws, traditionally used to simulate cell mechanical behaviour, are not appropriate for untreated contractile cells, and their use should be limited to the simulation of cells in which the active force generation machinery of the actin cytoskeleton has been chemically disrupted.

A computational analysis of cell-mediated compaction and collagen remodeling in tissue-engineered heart valves

One of the most critical problems in heart valve tissue engineering is the progressive development of valvular insufficiency due to leaflet retraction. Understanding the underlying mechanisms of this process is crucial for developing tissue-engineered heart valves (TEHVs) that maintain their functionality in the long term. In the present study, we adopted a computational approach to predict the remodeling process in TEHVs subjected to dynamic pulmonary and aortic pressure conditions, and to assess the risk of valvular insufficiency. In addition, we investigated the importance of the intrinsic cell contractility on the final outcome of the remodeling process. For valves implanted in the aortic position, the model predictions suggest that valvular insufficiency is not likely to occur as the blood pressure is high enough to prevent the development of leaflet retraction. In addition, the collagen network was always predicted to remodel towards a circumferentially aligned network, which is corresponding to the native situation. In contrast, for valves implanted in the pulmonary position, our model predicted that there is a high risk for the development of valvular insufficiency, unless the cell contractility is very low. Conversely, the development of a circumferential collagen network was only predicted at these pressure conditions when cell contractility was high. Overall, these results, therefore, suggest that tissue remodeling at aortic pressure conditions is much more stable and favorable compared to tissue remodeling at pulmonary pressure conditions.

Bioinspired polyethylene terephthalate nanocone arrays with underwater superoleophobicity and anti-bioadhesion properties

This paper presents a facile method to fabricate bioinspired polyethylene terephthalate (PET) nanocone arrays via colloidal lithography. The aspect ratio (AR) of the nanocones can be finely modulated ranging from 1 to 6 by regulating the etching time. The samples with the AR value of 6 can present underwater superoleophobicity with the underwater oil contact angle (OCA) of 171.8°. The as-prepared PET nanocone arrays perform anti-bioadhesion behavior, which inhibits the formation of the actin cytoskeleton when it used as the substrate for cell culture. Moreover, the oil wettability is temperature controlled after modifying the PET nanocone arrays with PNIPAAm film, and the oil wettability of the functionalized nanocone arrays can be transformed from the superoleophobic state with OCA about 151° to the oleophilic state with OCA about 25° reversibly. Due to the high-throughput, parallel fabrication and cost-efficiency of this method, it will be favourable for researchers to introduce oleophobic properties to various substrate and device surfaces. Due to the superoleophobicity and simple functionalizing properties, the PET nanocone arrays are very promising surfaces for anti-adhesion, self-cleaning and have potential applications in material, medical, and biological fields.

Probing cellular mechanoadaptation using cell-substrate de-adhesion dynamics: experiments and model

Physical properties of the extracellular matrix (ECM) are known to regulate cellular processes ranging from spreading to differentiation, with alterations in cell phenotype closely associated with changes in physical properties of cells themselves. When plated on substrates of varying stiffness, fibroblasts have been shown to exhibit stiffness matching property, wherein cell cortical stiffness increases in proportion to substrate stiffness up to 5 kPa, and subsequently saturates. Similar mechanoadaptation responses have also been observed in other cell types. Trypsin de-adhesion represents a simple experimental framework for probing the contractile mechanics of adherent cells, with de-adhesion timescales shown to scale inversely with cortical stiffness values. In this study, we combine experiments and computation in deciphering the influence of substrate properties in regulating de-adhesion dynamics of adherent cells. We first show that NIH 3T3 fibroblasts cultured on collagen-coated polyacrylamide hydrogels de-adhere faster on stiffer substrates. Using a simple computational model, we qualitatively show how substrate stiffness and cell-substrate bond breakage rate collectively influence de-adhesion timescales, and also obtain analytical expressions of de-adhesion timescales in certain regimes of the parameter space. Finally, by comparing stiffness-dependent experimental and computational de-adhesion responses, we show that faster de-adhesion on stiffer substrates arises due to force-dependent breakage of cell-matrix adhesions. In addition to illustrating the utility of employing trypsin de-adhesion as a biophysical tool for probing mechanoadaptation, our computational results highlight the collective interplay of substrate properties and bond breakage rate in setting de-adhesion timescales.

Airway smooth muscle in asthma: linking contraction and mechanotransduction to disease pathogenesis and remodelling

Asthma is an obstructive airway disease, with a heterogeneous and multifactorial pathogenesis. Although generally considered to be a disease principally driven by chronic inflammation, it is becoming increasingly recognised that the immune component of the pathology poorly correlates with the clinical symptoms of asthma, thus highlighting a potentially central role for non-immune cells. In this context airway smooth muscle (ASM) may be a key player, as it comprises a significant proportion of the airway wall and is the ultimate effector of acute airway narrowing. Historically, the contribution of ASM to asthma pathogenesis has been contentious, yet emerging evidence suggests that ASM contractile activation imparts chronic effects that extend well beyond the temporary effects of bronchoconstriction. In this review article we describe the effects that ASM contraction, in combination with cellular mechanotransduction and novel contraction-inflammation synergies, contribute to asthma pathogenesis. Specific emphasis will be placed on the effects that ASM contraction exerts on the mechanical properties of the airway wall, as well as novel mechanisms by which ASM contraction may contribute to more established features of asthma such as airway wall remodelling.

The direction of stretch-induced cell and stress fiber orientation depends on collagen matrix stress

Cell structure depends on both matrix strain and stiffness, but their interactive effects are poorly understood. We investigated the interactive roles of matrix properties and stretching patterns on cell structure by uniaxially stretching U2OS cells expressing GFP-actin on silicone rubber sheets supporting either a surface-adsorbed coating or thick hydrogel of type-I collagen. Cells and their actin stress fibers oriented perpendicular to the direction of cyclic stretch on collagen-coated sheets, but oriented parallel to the stretch direction on collagen gels. There was significant alignment parallel to the direction of a steady increase in stretch for cells on collagen gels, while cells on collagen-coated sheets did not align in any direction. The extent of alignment was dependent on both strain rate and duration. Stretch-induced alignment on collagen gels was blocked by the myosin light-chain kinase inhibitor ML7, but not by the Rho-kinase inhibitor Y27632. We propose that active orientation of the actin cytoskeleton perpendicular and parallel to direction of stretch on stiff and soft substrates, respectively, are responses that tend to maintain intracellular tension at an optimal level. Further, our results indicate that cells can align along directions of matrix stress without collagen fibril alignment, indicating that matrix stress can directly regulate cell morphology.